One approach is to use the Double Matrix Method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of students, and the two characteristics are:
- passed math for didn't pass math
- passed physics or didn't pass physics

Aside: We can also use Venn diagrams and formulae to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method works every time.

Given: 80% of the students passed Mathematics
So, if we let x = the total number of students, then 0.8x = the total number of students that passed mathematics.
If 80% of the students passed mathematics, then 20% of the x students failed.
So, 0.2x = the total number of students that failed mathematics.
So, we can set up our Matrix as follows:



Given: The number of students who passed Mathematics is 120 more than the number of students who passed in Physics.
In other words, the number of students who passed physics is 120 less than the number of students who passed math.
So, the number of students who passed physics = 0.8x - 120
If there are x students in total, and 0.8x - 120 of them passed physics, then the number of students who failed physics = x - (0.8x - 120) = 0.2x + 120
So, we have:



Given: 180 students passed in both subjects.
So, we have:



At this point we can populate the remaining boxes.
Since the two TOP boxes must add to 0.8x, the top right box = 0.8x - 180.
Since the two boxes on the LEFT side must add to 0.8x - 120, the bottom left box = (0.8x - 120) - 180 = 0.8x - 300.
Since the two BOTTOM boxes must add to 0.2x, the bottom right box = 0.2x - (0.8x - 300) = 300 - 0.6x.
So we have:


Given: The ratio of students who passed only in Physics and only in Mathematics was 1:7
So we get the following equation: (0.8x - 300)/(0.8x - 180) = 1/7
Cross multiply to get: 5.6x - 2100 = 0.8x - 180
Rearrange to get: 4.8x = 1920
Solve: x = 400

We know that the number of students who failed both courses = 300 - 0.6x,
Plug in x = 400 to get: 300 - 0.6(400) = 300 - 240 = 60

Answer: C